What is "signing a message" in when connecting wallet?

Signing a message is basically encrypting a string using your wallet. Like on-chain messaging.

This is typically used to check the ownership of a wallet in many websites / dapps.

However malcious developers or websites can request you to sign a string and this string can be something like sending ETH or swapping ETH to random tokens etc.

Make sure to read what string they request to sign and always avoid something like signing function style strings like swapExactETH(...) or Multicall() etc.

Our Dapp requests you to sign insidor_dapp string which is used to encrypt your private key of new accounts to store on your local storage.

Always make sure you make a backup of these accounts.